Higher Interpolation and Extension for Persistence Modules

DOI10.1137/16M1100472zbMath1421.55003arXiv1603.07406MaRDI QIDQ5283248

Peter Bubenik, Vidit Nanda, Vin De Silva

Publication date: 21 July 2017

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.07406

zbMATH Keywords

Lipschitz extensionspersistent homologyKan extensions

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Other homology theories in algebraic topology (55N35)

Related Items (5)

Generalized persistence diagrams ⋮ Connectedness and Lusternik-Schnirelmann categories of the spaces of persistence modules ⋮ Bottleneck stability for generalized persistence diagrams ⋮ Computational Complexity of the Interleaving Distance ⋮ Topological spaces of persistence modules and their properties

Cites Work

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• Topological signals of singularities in Ricci flow
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• The Structure and Stability of Persistence Modules
• Topology and data
• Simplicial Models and Topological Inference in Biological Systems
• Decomposition of pointwise finite-dimensional persistence modules
• Geometry in the space of persistence modules
• Proximity of persistence modules and their diagrams
• Statistical topological data analysis using persistence landscapes
• Barcodes: The persistent topology of data

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